Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41. Using the empirical rule, what percentage of the students have grade point averages that are between 2.2 and 3.02?

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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with
a mean of 2.61 and a standard deviation of 0.41. Using the empirical rule, what percentage of the students have
grade point averages that are between 2.2 and 3.02?
Transcribed Image Text:Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41. Using the empirical rule, what percentage of the students have grade point averages that are between 2.2 and 3.02?
Expert Solution
Step 1

Empirical rule:

  • The probability that the observation under the normal curve lies within 1 standard deviation of the mean is approximately 0.6826.
  • The probability that the observation under the normal curve lies within 2 standard deviations of the mean is approximately 0.9544.
  • The probability that the observation under the normal curve lies within 3 standard deviations of the mean is approximately 0.9973.
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